Problem: Recently Duff has been a soldier in the army. Malek is her commander.

Their country, Andarz Gu has n cities (numbered from 1 to n) and n - 1 bidirectional roads. Each road connects two different cities. There exist a unique path between any two cities.

There are also m people living in Andarz Gu (numbered from 1 to m). Each person has and ID number. ID number of i - th person is i and he/she lives in city number ci. Note that there may be more than one person in a city, also there may be no people living in the city.

<image>

Malek loves to order. That's why he asks Duff to answer to q queries. In each query, he gives her numbers v, u and a.

To answer a query:

Assume there are x people living in the cities lying on the path from city v to city u. Assume these people's IDs are p1, p2, ..., px in increasing order. 

If k = min(x, a), then Duff should tell Malek numbers k, p1, p2, ..., pk in this order. In the other words, Malek wants to know a minimums on that path (or less, if there are less than a people).

Duff is very busy at the moment, so she asked you to help her and answer the queries.

Input

The first line of input contains three integers, n, m and q (1 ≤ n, m, q ≤ 105).

The next n - 1 lines contain the roads. Each line contains two integers v and u, endpoints of a road (1 ≤ v, u ≤ n, v ≠ u).

Next line contains m integers c1, c2, ..., cm separated by spaces (1 ≤ ci ≤ n for each 1 ≤ i ≤ m).

Next q lines contain the queries. Each of them contains three integers, v, u and a (1 ≤ v, u ≤ n and 1 ≤ a ≤ 10).

Output

For each query, print numbers k, p1, p2, ..., pk separated by spaces in one line.

Examples

Input

5 4 5
1 3
1 2
1 4
4 5
2 1 4 3
4 5 6
1 5 2
5 5 10
2 3 3
5 3 1


Output

1 3
2 2 3
0
3 1 2 4
1 2

Note

Graph of Andarz Gu in the sample case is as follows (ID of people in each city are written next to them):

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
double esp = 1e-12;
const double PI = acos(-1.0);
const long long int INF = 0x3f3f3f3f3f3f3f3f;
const int MOD = 1000000007;
int dx[8] = {1, 0, -1, 0, 1, 1, -1, -1};
int dy[8] = {0, 1, 0, -1, 1, -1, 1, -1};
int POS;
struct treepo {
  static const int MAXN = 100050;
  struct SegTree {
    int n;
    struct Node {
      int h[11];
    } nd[MAXN << 2];
    Node PushUp(Node u, Node v) {
      int i = 0, j = 0;
      Node w;
      memset(w.h, 0, sizeof(w.h));
      while (1) {
        if (i + j == 11) return w;
        if (u.h[i] == 0 && v.h[j] == 0) return w;
        if (u.h[i] == 0) {
          w.h[i + j] = v.h[j];
          j++;
        } else if (v.h[j] == 0) {
          w.h[i + j] = u.h[i];
          i++;
        } else {
          if (u.h[i] < v.h[j]) {
            w.h[i + j] = u.h[i];
            i++;
          } else {
            w.h[i + j] = v.h[j];
            j++;
          }
        }
      }
      return w;
    }
    void PushUp(int rt) { nd[rt] = PushUp(nd[rt << 1], nd[rt << 1 | 1]); }
    void build(int l, int r, int rt) {
      memset(nd[rt].h, 0, sizeof(nd[rt].h));
      if (l == r) {
        memset(nd[rt].h, 0, sizeof(nd[rt].h));
        return;
      }
      int m = (l + r) >> 1;
      build(l, m, rt << 1);
      build(m + 1, r, rt << 1 | 1);
      PushUp(rt);
    }
    void build(int n) {
      this->n = n;
      build(1, n, 1);
    }
    void update(int L, int c, int l, int r, int rt) {
      if (L <= l && r <= L) {
        int tem = c;
        for (int x = 0; x <= 10; x++)
          if (nd[rt].h[x]) {
            if (nd[rt].h[x] > c) swap(tem, nd[rt].h[x]);
          } else {
            swap(tem, nd[rt].h[x]);
            break;
          }
        return;
      }
      int m = (l + r) >> 1;
      if (L <= m) update(L, c, l, m, rt << 1);
      if (m < L) update(L, c, m + 1, r, rt << 1 | 1);
      PushUp(rt);
    }
    void update(int L, int c) { update(L, c, 1, n, 1); }
    Node query(int L, int R, int l, int r, int rt) {
      if (L <= l && r <= R) {
        return nd[rt];
      }
      int m = (l + r) >> 1;
      Node mc;
      memset(mc.h, 0, sizeof(mc.h));
      if (L <= m) mc = PushUp(mc, query(L, R, l, m, rt << 1));
      if (m < R) mc = PushUp(mc, query(L, R, m + 1, r, rt << 1 | 1));
      return mc;
    }
    Node query(int L, int R) { return query(L, R, 1, n, 1); }
  } tr;
  struct Edge {
    int to, next;
  } edge[MAXN * 2];
  int head[MAXN], tot;
  int top[MAXN];
  int fa[MAXN];
  int deep[MAXN];
  int num[MAXN];
  int p[MAXN];
  int fp[MAXN];
  int son[MAXN];
  void init(int n) {
    tot = 0;
    memset(head, -1, sizeof(head));
    POS = 1;
    memset(son, -1, sizeof(son));
    tr.build(n);
  }
  void addedge(int u, int v) {
    edge[tot].to = v;
    edge[tot].next = head[u];
    head[u] = tot++;
    edge[tot].to = u;
    edge[tot].next = head[v];
    head[v] = tot++;
  }
  void dfs1(int u, int pre, int d) {
    deep[u] = d;
    fa[u] = pre;
    num[u] = 1;
    for (int i = head[u]; i != -1; i = edge[i].next) {
      int v = edge[i].to;
      if (v != pre) {
        dfs1(v, u, d + 1);
        num[u] += num[v];
        if (son[u] == -1 || num[v] > num[son[u]]) son[u] = v;
      }
    }
  }
  void dfs1() { dfs1((tr.n + 1) / 2, -1, 0); }
  void getPOS(int u, int sp) {
    top[u] = sp;
    p[u] = POS;
    POS++;
    fp[p[u]] = u;
    if (son[u] == -1) return;
    getPOS(son[u], sp);
    for (int i = head[u]; i != -1; i = edge[i].next) {
      int v = edge[i].to;
      if (v != son[u] && v != fa[u]) getPOS(v, v);
    }
  }
  void getPOS() { getPOS((tr.n + 1) / 2, (tr.n + 1) / 2); }
  SegTree::Node qu(int va, int vb) {
    if (va == vb) return tr.query(p[va], p[va]);
    SegTree::Node ans;
    memset(ans.h, 0, sizeof(ans.h));
    int f1 = top[va], f2 = top[vb];
    while (f1 != f2) {
      if (deep[f1] < deep[f2]) {
        swap(f1, f2);
        swap(va, vb);
      }
      ans = tr.PushUp(ans, tr.query(p[f1], p[va]));
      va = fa[f1];
      f1 = top[va];
    }
    if (va == vb) return tr.PushUp(ans, tr.query(p[va], p[va]));
    if (deep[va] < deep[vb]) swap(va, vb);
    return tr.PushUp(ans, tr.query(p[vb], p[va]));
  }
} pt;
int main() {
  int n, m, q, u, v, tem, a;
  scanf("%d%d%d", &n, &m, &q);
  pt.init(n);
  for (int x = 1; x <= n - 1; x++) {
    scanf("%d%d", &u, &v);
    pt.addedge(u, v);
  }
  pt.dfs1();
  pt.getPOS();
  for (int x = 1; x <= m; x++) {
    scanf("%d", &tem);
    pt.tr.update(pt.p[tem], x);
  }
  treepo::SegTree::Node ans;
  int len = 0;
  for (int x = 1; x <= q; x++) {
    len = 0;
    scanf("%d%d%d", &u, &v, &a);
    ans = pt.qu(u, v);
    for (int y = 0; y < a; y++)
      if (ans.h[y]) len++;
    len = min(len, a);
    printf("%d ", len);
    for (int y = 0; y < len; y++) printf("%d ", ans.h[y]);
    printf("\n");
  }
  return 0;
}